Is there any sound basis for the claim that devils are attached to doorsteps and concentrated at their entrances?

We do not know of any evidence to support the validity of your husband's mother's statement. The texts indicate that protection from Satan is achieved through remembrance (dhikr) upon entering the home, the importance of closing doors at night, and that Satan does not open a closed door. Muslim narrated from Jabir ibn Abdullah that the Prophet, peace and blessings be upon him, said: "When a man enters his house and remembers Allah upon entering and upon eating, Satan says: 'You have no place to sleep and no supper.' And if he enters and does not remember Allah upon entering, Satan says: 'You have found a place to sleep.' And if he does not remember Allah upon his food, Satan says: 'You have found a place to sleep and supper.'" And Muslim narrated from Jabir from the Messenger of Allah, peace and blessings be upon him, that he said: "Cover the vessel, tie the waterskin, close the door, and extinguish the lamp; for Satan does not untie a waterskin, nor open a door, nor uncover a vessel. If one of you finds nothing but to place a stick across his vessel and mention the name of Allah, let him do so." Al-Hafiz Ibn Hajar said: "Indeed, Satan does not open a closed door" is an indication that the command to close doors is for the benefit of keeping Satan away from mingling with humans.